Physical Modeling: Introduction

Physical modeling emulates actual physical processes with digital means - oscillators, resonators and acoustic impedance are modeled with buffers and filters, respectively LTI systems. Although first realized when computers had sufficient power, the foundations are much older. Hiller et al. (1971) were the first to transport the 1774 wave equation by d'Alambert to the digital domain for synthesizing sounds of plucked strings.

Early Hardware

Although physical modeling algorithms sound great, offer good means for control and enable the design of interesting instruments, their had less impact on the evolution of music and digital instruments. Hardware synths for physical modeling from the 1990s, like the Korg Prophecy or the Yamaha VL1 did not become a success, in the first place. There are many possible reasons for the lack of success. Cheaper and larger memory made sampling instruments more powerful and virtual analog synthesizers sounded more attractive, followed by the second wave of analog synths.

Yamaha VL1 (1994)

Software Instruments

  • Pianoteq Pro 6
  • Organteq Alpha
  • Strum GS 2
  • AAS Chromophone 2


Since simple physical models are easily implemented on small embedded systems, various modules exist on the market:


Physical Models in Experimental Music

Eikasia (1999) by Hans Tutschku was realized using the IRAM software Modalys:


  • Vesa Välimäki. Discrete-time modeling of acoustic tubes using fractional delay filters. Helsinki University of Technology, 1995.
  • Gijs de Bruin and Maarten van Walstijn. Physical models of wind instruments: A generalized excitation coupled with a modular tube simulation platform*. Journal of New Music Research, 24(2):148–163, 1995.
  • Matti Karjalainen, Vesa Välimäki, and Zoltán Jánosy. Towards High-Quality Sound Synthesis of the Guitar and String Instruments. In Computer Music Association, 56–63. 1993.
  • Julius O Smith. Physical modeling using digital waveguides. Computer music journal, 16(4):74–91, 1992.
  • Lejaren Hiller and Pierre Ruiz. Synthesizing musical sounds by solving the wave equation for vibrating objects: part 1. Journal of the Audio Engineering Society, 19(6):462–470, 1971.
  • Lejaren Hiller and Pierre Ruiz. Synthesizing musical sounds by solving the wave equation for vibrating objects: part 2. Journal of the Audio Engineering Society, 19(7):542–551, 1971.

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